Magnetic resonance imaging (“MRI”) is commonly employed for clinical diagnostic imaging. Recent developments in quantitative MRI of reservoir rock core plugs have led to the development of new core analysis methods for capillary pressure and other petro-physical parameters [1-4]. An essential element in quantitative MRI of such systems is a reliable measure of fluid quantity in the pore space. Quantitative imaging is impaired in many cases by non-uniform radio frequency (RF) magnetic fields (typically referred to as “B1 fields”) in the sample space of MRI.
In MRI, it is frequently observed that naturally uniform samples do not have uniform image intensities. In many cases this non-uniform image intensity is due to an inhomogeneous B1 field. According to the ‘principle of reciprocity’ [5,6], the received MR signal for each point in space is proportional to the local B1 field strength per unit excitation current. The spatial variation of the RF field sensitivity for excitation and reception is one principal reason for non-uniform images of nominally uniform samples. Non-uniformities across the MRI image will affect the image-based quantification and interpretation of porous media.
One may solve the B1 inhomogeneity problem by limiting the sample space in a larger RF probe [7] but this is not a very good employment of the experimental sample space that is costly and at a premium. Prior art methods exist for determining the B1 field. When the information is determined or presented in the form of a two dimensional (2D) or three dimensional (3D) spatial distribution, it is called a B1 map. In quantitative MRI, one solution is to measure an absolute B1 map and correct the intensity inhomogeneities that arise from B1 variation [8-15].
Mapping of the B1 field can be undertaken with a wide variety of MRI-based methods. With double angle techniques [14, 16-17], B1 maps are acquired by measurement of the magnitude of the signal after α or 2α excitations. The imaging technique is usually based on spin echo imaging or echo planar imaging. One method is based on acquisition of a spin echo and a stimulated echo and the local B1 is determined by the ratio of images [18]. Actual flip angle imaging (AFI), employs FLASH imaging [19] with the interleaved acquisition of two echoes, applying the same flip angle but for different repetition times [20, 21]. The phase sensitive method for B1 mapping employs a series of RF pulses that generate a transverse magnetization whose phase is a function of the flip angle [22]. If a method is based on gradient echo imaging with large excitation angles, signal intensity variations are produced by employing flip angles that are distributed around 180° [23]. B1 mapping employing the Bloch-Siegert shift idea [24, 25] is one of the latest B1 mapping methods, mostly employed in clinical diagnostic imaging.
B1 mapping methods that are based on frequency encoding, such as all of the above methods, may suffer from B0 inhomogeneity artifacts.
Many methods have been developed to correct non-uniform MRI images due to B1 inhomogeneity [8-15, 29-33]. These image intensity correction methods either focus on the true image or the sensitivity profile because a natural assumption is that the final image is the true image multiplied by a sensitivity function of the system [11].